Analysis of DC-DC Converters by Averaging Method based on Lagrange Theorems

This paper presents a new approach for generating the state-space averaged model of dc-dc converters in the basis of relative variables using the Lagrange theorems. Averaged mathematical models of boost, buck and buck-boost converters have been developed, allowing the analysis of steady-state processes in continuous conduction mode (CCM) and discontinuous conduction mode (DCM). It is shown that a new approach to obtaining averaged models makes it possible to calculate not only the constant components of the process, but also their pulsation components, as well as the duration of the time intervals of the steady-state process, which is an advantage over traditional averaging methods. Using the obtained models, the dependences of the current ripple of the storage choke relative to the load current and the voltage transfer coefficient of the converters were calculated in the entire range of regulation of the switching duration.